Mixed spin-1/2 and spin-1 Ising model on a bilayer hierarchical lattice

A study of mixed spin-1/2 and spin-1 Ising model on "folded" square lattice model was carried out using the previously proposed general approach for renormalization group transformations. Considering the symmetries of the model, the study was divided into ferromagnetic and antiferromagnetic cases. We found that the critical points of the renormalization group transformation for a low-temperature phase transition are unstable at any value of the intralayer interactions and nonzero interlayer interaction in the ferromagnetic case. However, in the antiferromagnetic case this is observed only for one phase. In addition, the magnitude of the shift exponent was calculated for each of the cases. As in the two-layer spin-1/2 Ising model, it has a singularity only at certain parameters and only in the ferromagnetic case. In other cases, the magnitude of the shift exponent is close to 0.5.